Source Poverty and Canonical Admissibility in Fibered Descent Systems
Year: 2026
Type: preprint
Abstract: Three independently discovered collapse phenomena — in monadic model theory, categorical semantics, and topos theory — share a common fibered descent structure. In each case, target content is constrained to a canonically determined admissible region computed from a source, and collapse occurs when the source is informationally trivial. We identify two modes of canonical admissibility: a reflective fixed-point mode (available when round-trip transport exists) and a descent-equalizer mode (available for quotient-type transports). Both yield a Level-1 raw capacity law: the number of raw admissible configurations equals v^d, where v is the value base and d is the source slot count; Level-2 coherence constraints remain case-specific. Collapse is the degenerate case d = 0. Two of the three collapse results — from monadic model theory and topos theory — are further unified as instances of the same categorical construction (pushforward in the subobject bifibration). We classify the descent conditions by morphism type and identify a stratification into raw capacity (Level 1, unified) and coherence constraints (Level 2, case-specific).
Authors: Badkur, Prashi, Dak, Mohit
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162039371
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